Can tip plasty help with breathing problems?

Great question!  Unfortunately, tip refinement will not help with any functional breathing issues, unless your ala is collapsing and needs support.  Otherwise when it comes to functional breathing issues, its either the septum or the turbinates that are causing you to have difficulty breathing, so one or both of these structures need modification.Best of luck and hope this information helps!
- Dr. Roger Tsai  @DrRogerTsai
Board Certified Plastic Surgeon

Hello,Thanks for your question. Yes, there are situations in which tip rhinoplasty is helpful at improving functional breathing problems. One is the situation of a plunging tip that block anterior airflow a bit. A tip rhinoplasty the rotates the tip and supports it allows for more direct travel of air into the nostrils. Another situation occurs after an initial rhinoplasty in which scarring narrows the airway. Tip surgery to debulk scar and reopen the airway can often be successful for certain patients. Dr. Shah

When the tip cartilages are strong enough to make the tip look wide and prominent, they often are also strong enough to hold the tip down, making the tip droop. When the tip is worked on, the tip elevates at the same time that it becomes narrower. The woman in the short video that I posted with this answer had a wide tip that was elevated significantly in her rhinoplasty.
When the tip comes up, it can often make breathing easier. It depends on many factors, but it's certainly not unknown.
Remember that rhinoplasty is an exquisitely difficult operation to get right, and you should only have surgery if you are able to make yourself very confident in your surgeon's skills. The changes I described above require advanced techniques, requiring skill that most plastic surgeons don't possess with expertise. For most noses, it's much better to not have surgery than to have inexpertly-performed surgery. Read my essay on how to stay out of trouble while selecting a rhinoplasty surgeon. 
Your nose is also a perfect example of why computer imaging is mandatory in rhinoplasty. You need to know exactly what the surgeon is planning to accomplish -- what features he thinks he can change, and by how much he thinks he can change them. I always email morphs to my online rhinoplasty consultations. When you see the surgeon's goals in the morphs, you'll know whether he has an eye for an attractive nose, and whether he shares your opinion of what constitutes an attractive nose. You'll also know whether the changes he proposes are large enough to be meaningful to you, and whether he understands your wishes enough to address all of your priorities. How would you ever get that figured out without the morphs?! 
But remember, you're not the surgeon for his skills with the computer. The doctor must then show you his before and after photos to prove that he can actually accomplish what he draws on the computer.